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%I #13 Oct 07 2015 16:18:00
%S 373,10363,61723,210901,539041,1151983,2180263,3779113,6128461,
%T 9432931,13921843,19849213,27493753,37158871,49172671,63887953,
%U 81682213,102957643,128141131,157684261,192063313,231779263,277357783,329349241
%N a(n) = 373 + 1947n + 3780n^2 + 3234n^3 + 1029n^4.
%C A000540(n) is divisible by A000330(n) if and only n is congruent to {1,2,4,5} mod 7 (see A047380) A134158 is case when n is congruent to 1 mod 7 A134159 is case when n is congruent to 2 mod 7 A134160 is case when n is congruent to 4 mod 7 A134161 is case when n is congruent to 5 mod 7 A133180 is union of A134158 and A134159 and A134160 and A134161
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).
%F a(n) = (3(7n + 5)^4 + 6(7n + 5)^3 - 3 (7n + 5) + 1)/7 a(n) = Sum[k^6]/Sum[k^2], {k, 1, 7n + 5}]
%F G.f.: -(373+8498*x+13638*x^2+2186*x^3+x^4)/(-1+x)^5. - _R. J. Mathar_, Nov 14 2007
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) with a(0)=373, a(1)=10363, a(2)=61723, a(3)=210901, and a(4)=539041. - _Harvey P. Dale_, Nov 25 2012
%t 1) Table[(3(7n + 5)^4 + 6(7n + 5)^3 - 3 (7n + 5) + 1)/7, {n, 0, 100}] 2) Table[Sum[k^6, {k, 1, 7n + 5}]/Sum[k^2, {k, 1, 7n + 5}], {n, 0, 100}] (*Artur Jasinski*)
%t LinearRecurrence[{5,-10,10,-5,1},{373,10363,61723,210901,539041},100] (* _Harvey P. Dale_, Nov 25 2012 *)
%o (PARI) a(n)=373+1947*n+3780*n^2+3234*n^3+1029*n^4 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A000330, A000540, A119617, A134153, A134154, A133180, A134158, A134159, A134160.
%K nonn,easy
%O 0,1
%A _Artur Jasinski_, Oct 10 2007
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